U.S. patent number 4,257,006 [Application Number 06/006,438] was granted by the patent office on 1981-03-17 for integrable analog active filter and method of same.
This patent grant is currently assigned to The Regents of the University of Minnesota. Invention is credited to Rolf Schaumann.
United States Patent |
4,257,006 |
Schaumann |
March 17, 1981 |
**Please see images for:
( Certificate of Correction ) ** |
Integrable analog active filter and method of same
Abstract
Integrable analog active filter suitable for MOS monolithic
implementation. The filter utilizes only integrating amplifiers and
ratioed capacitors thus being implementable in MOS technology and
compatible for use in MOS digital systems. Filters of unlimited
complexity and having arbitrary transfer functions can be
implemented by the integrable analog active filter.
Inventors: |
Schaumann; Rolf (Minnetonka,
MN) |
Assignee: |
The Regents of the University of
Minnesota (Minneapolis, MN)
|
Family
ID: |
21720887 |
Appl.
No.: |
06/006,438 |
Filed: |
January 25, 1979 |
Current U.S.
Class: |
327/336; 327/552;
330/107; 330/294; 333/213 |
Current CPC
Class: |
H03H
11/1217 (20130101) |
Current International
Class: |
H03H
11/04 (20060101); H03H 11/12 (20060101); H03B
001/04 (); H03F 001/08 (); H03F 001/56 (); H03H
002/00 () |
Field of
Search: |
;330/107,109,294
;328/127,167 ;333/213,214 ;307/233,304 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Heyman; John S.
Attorney, Agent or Firm: Peterson, Palmatier, Sturm &
Sjoquist, Ltd.
Government Interests
The Government has rights in this invention pursuant to Grant No.
NSF ENG 76-11218 awarded by the National Science Foundation.
Claims
Having thus described the invention, what is claimed is:
1. An active analog filter consisting, essentially, in
combination;
input and output terminals adapted for connection to a source of
signal and signal utilization means; and
integrating means effectively free of resistors in performing the
integrating operation interconnecting said input and output
terminals, said integrating means including amplifier means and
reactance means exhibiting resistorless capacitance
characteristics.
2. The subject matter of claim 1 in which the reactance means
includes a plurality of capacitors having interrelated values.
3. The subject matter of claim 1 in which further reactance means
and signal combining means are connected intermediate the input
terminal and said amplifier means and further reactance means are
connected intermediate the output terminal and said signal
combining means, all of said reactance means having interrelated
magnitudes.
4. The subject matter of claim 3 in which the integrating means
includes at least a pair of amplifier means and each of said
amplifier means is connected to said signal combining means through
a further reactance means.
5. The method of processing predetermined frequency components of
an analog signal comprising the steps of;
providing a plurality of reactance means exhibiting resistorless
capacitive characteristics;
providing a signal combining means;
providing a signal integrating means effectively free of resistors
in performing the integrating operation;
passing a signal through one of said reactance means, said signal
combining means and said integrating means while simultaneously
passing a signal from said integrating means to said signal
combining means.
6. The method of claim 5 in which the reactance means are selected
to have interrelated magnitudes.
7. The method of claim 6 in which the signal is passed through a
plurality of integrating means.
8. The method of claim 7 in which the signal is passed through a
successive plurality of integrating means.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to analog active filters,
and more particularly, pertains to integrable analog active filters
utilizing only integrating amplifiers and ratioed capacitors.
2. Description of the Prior Art
Recently, there has been considerable interest in the development
of active filters suitable for fully integrated monolithic
implementation. Standard active RC filter design has not been
normally useful for full integration because of the need for
capacitors which are too large for integrated circuit
technology.
Active R filters have received attention because they use
integrating amplifiers, no capacitors, and establish filter
parameters via ratios of resistors. Active R filters employ
capacitors for only internal amplifier compensation. In active R
filters, amplifiers are used as integrators and filter parameters
such as pole frequency, quality factor, and gain are established
with resistor ratios. Active R filters have the advantage of being
suitable for operation over wide ranges of frequency, audio to
video, but are prone to drifts, and use relatively large amounts of
silicon area. Although the active R filters are easy to realize in
integrated circuit technology, resistor ratios are less
advantageous than ratios of capacitors for integrated circuit
implementation, especially in MOS form.
Sampled-data analog switched-capacitor filters in which resistors
are simulated via switched capacitors have been shown to perform
very well at low frequencies but operation at high frequencies is
far less than satisfactory because of problems associated with the
need for very high switching frequency to avoid aliasing, with
switching noise, and with the finite charging and discharging time
of the capacitors. At the high frequencies, the internal amplifier
dynamics introduce additional poles and phase shifts giving rise in
switched-capacitor filters to the same problems encountered in
active RC filters at the high frequencies.
With few exceptions, none of them useful for MOS implementation,
filters which have been fully implemented in integrated form to
date are either digital in nature or belong to the class of sampled
data filters, such as switched-capacitor circuits. None of the
prior art filters are readily integrable in MOS technology, and,
thus, lack compatibility with modern integrated digital signal
processing systems.
The integrable analog active filter proposed in this invention
avoids most of the problems of the prior art filters.
SUMMARY OF THE INVENTION
The general purpose of the present invention is to provide an
integrable analog active filter which in addition to utilizing
integrating amplifiers utilizes only ratios of small capacitors for
the synthesis of filter transfer functions.
According to one preferred embodiment of the present invention,
there is provided an integrable analog active filter of at least
second order having two integrating amplifiers connected to a loop
and ratioed capacitors connected between the output and the input
of the first amplifier, between the output of the second amplifier
and the input of the first amplifier, and to the input of the first
amplifier whereby said ratioed capacitors connected across the
integrating amplifiers provide an MOS integrable analog active
filter.
It is a principal object of the present invention to provide an
integrable analog active filter implementable as a fully monolithic
analog active filter, especially in MOS technology, utilizing MOS
amplifiers and ratios of MOS capacitors. Implementations using only
MOS transistors and capacitors are also possible. The resistors
necessary for biasing and direct current stabilization can be
realized with MOS transistors or via a leaky dielectric, and are
thus compatible with MOS technology.
A further object of the present invention is an invention which is
equally well suited for low frequency and for high frequency analog
active filters. Further advantages of the invention are the ratios
of the capacitors utilize less silicon area than resistor ratios;
the capacitors are more accurate and less prone to drift due to
temperature, voltage level, and aging; the capacitors are small,
down to values where parasitics become significant; in carefully
designed monolithic realizations, capacitors of fractions of
picofarads are feasible, parasitic capacitors can be readily
accounted for by absorbing the same into existing capacitors. Also,
the circuit internal amplifier loads are negligible until very high
frequency operation is reached. Further, the noise performance of
the integrable analog active filter is superior because of the
elimination of circuit resistors.
An additional object of the present invention is to provide an
integrable analog active filter, thus eliminating all switchng
circuitry, timing functions, biasing problems, and switching noise.
Also, the integrable analog active filter is more suitable for high
frequency operation by eliminating switching problems, difficulties
related to capacitor charging and discharging times, and by
including the major amplifier "parasitic", the gain rolloff,
directly into the design procedure.
Applications of the present invention are integrable,
technology-compatible, band limiting filters for sampled-data or
digital signal processing applications; further applications are in
high-precision filtering needs in low and high frequency analog
communications.
BRIEF DESCRIPTION OF THE DRAWINGS
Other objects and many of the attendant advantages of this
invention will be readily appreciated as the same becomes better
understood by reference to the following detailed description when
considered in connection with the accompanying drawings, in which
like reference numerals designate like parts throughout the figures
thereof and wherein:
FIG. 1 illustrates a general "two-integrator" class circuit;
FIGS. 2a and 2b illustrate implementations of integrator A.sub.2 of
FIG. 1;
FIGS. 3a and 3b illustrate implementations of integrator A.sub.1
and of the summer of FIG. 1;
FIGS. 4a and 4b illustrate possible embodiments of integrable
analog active all-capacitor filters, and;
FIG. 5 illustrates a special case of the implementation in FIG. 4a
with an added MOS output summing circuit.
DESCRIPTION OF PREFERRED EMBODIMENTS
The state-variable-derived topology of the circuit 10 of FIG. 1
yields the equations
where constants a, b, and c are implemented via the capacitor
ratios as later described.
The two amplifiers, A.sub.1 and A.sub.2, are identical and
described by the single-pole function for the gain ##EQU1## where
GB is the gain-bandwidth product, .sigma. the 3dB-frequency, and
the "excess phase" term exp (-s.tau.) accounts for the effect of
additional poles and zeros of A(s). If the two amplifiers A.sub.1
and A.sub.2 are not identical, the result is not significantly
different. Since the frequency of operation, .omega., satisfies
.omega.>>.sigma., the amplifiers are ideal integrators in a
normalized frequency parameter S=s/GB, and T is defined as
T=.tau.GB. Where T=0, eqs. 1 and 2 indicate that the circuit
configuration of FIG. 1 yields the bandpass and low pass
functions
The actual implementation of the block diagrams of FIG. 1 realizes
the circuits of FIGS. 2a and 2b which are considered for amplifier
A.sub.2 and the circuits of FIGS. 3a 3b for the amplifier A.sub.1,
including the summer 12.
The circuit in FIG. 2a realizes, with equation 2 and T=0,
where
Similarly, for FIG. 2b, V.sub.L =-c.sub.2 S.sup.-1 V.sub.B.
FIG. 3a yields
with
where Y.sub.1 -Y.sub.7 are admittances.
Similarly, FIG. 3b is described by equations 6 and 7 where
Thus, second-order filters are realized by connecting FIGS. 2a and
3a, or FIGS. 2b and 3b.
All filter parameters are determined by ratios of admittances
which, especially in integrated circuit form, can be implemented
conveniently with ratios of small capacitors. Thus from FIGS. 2a
and 3a, and, respectively, from FIGS. 2b and 3b, the two
all-capacitor active filter structures in FIGS. 4a and 4b are
obtained; FIG. 4a yields
and FIG. 4b:
The capacitor ratios a.sub.k, b, c.sub.1k, c.sub.2, k=1, 2, are
given by equations 5, 7, and 8 with Y.sub.i =sC.sub.i.
The resistors R.sub.2, R.sub.4, and R.sub.7 of FIG. 4a and R.sub.2,
R.sub.5, and R.sub.7 of FIG. 4b illustrated with dashed connections
in FIGS. 4a and 4b respectively provide bias currents to the
amplifier inputs and implement direct current feedback for
stability. Their exact values are not critical; the resistors are
chosen large, and in monolithic form, are implemented with pinched
resistors, as spreading resistance, via a leaky dielectric or as
suitably biased transistors.
The circuits in FIGS. 4a and 4b yield second-order lowpass and
bandpass filters of positive or negative gain. Biquadratic transfer
functions are available at the inverting input terminals of
amplifier A.sub.1 in FIGS. 4a and 4b.
The following considers only the circuit of FIG. 4a described by
equations 9a and 9b with 5 and 7, as FIG. 4b is similar to FIG. 4a.
The illustration of FIG. 4b is completely analogous to FIG. 4a.
From equations 9a and 9b,
where .omega..sub.o is the pole frequency and Q the pole quality
factor. Thus, with equations 5 and 7,
Further, from equations 9a and 9b, respectively, the mid-band gain
H.sub.B and direct current gain H.sub.L equal
Depending on whether the desired gain is positive or negative,
equation 13 together with equation 12 can be solved for the
necessary capacitor ratios.
For example, a bandpass filter with negative gain results in
a.sub.1 =0 where C.sub.4 =0, C.sub.5 =.infin.. From equation 13,
H.sub.B =-a.sub.2 /b =-C.sub.1 /C.sub.3. For this type of filter,
the capacitor ratio equations with equation 12 are
A simplification of the circuit is obtained by setting c.sub.2 =1
where C.sub.6 =.infin., C.sub.7 =0. This eliminates two capacitors
and results in the capacitor ratio equations
The values of .OMEGA..sub.o, Q and H.sub.B are inserted into
equations 11-15 for a correct design. In this choice of parameters,
the amplifiers'excess phase, -.OMEGA.T, introduced in equation 2,
is taken into account. The effects are analyzed by inserting
equation 2 into equation 1a where ##EQU2## The phase term in the
numerator of equation 16 adds to the total phase of T.sub.B (S).
The exponential terms in the denominator are shown to give rise to
Q and gain enhancement, and to a small perturbation of the pole
frequency according to
where .OMEGA..sub.R, Q.sub.R and H.sub.BR are the realized
parameters and .OMEGA..sub.o, Q and H.sub.B the designed ones.
Equations 17a-c then provides the predistorted values
.OMEGA..sub.o, Q and H.sub.B to be used in equations 12a, 12b, 13,
14a-14c, 15a and 15b which for a given T result in .OMEGA..sub.R,
Q.sub.R and H.sub.BR. The approximations are valid for
4Q.sub.R.sup.2 >>1 and 2Q.sub.R >> tan .OMEGA..sub.R
T.
The sensitivity of a filter parameter k to an element x,
S.sub.x.sup.k =(dk/k)/(dx/x), is determined from equations 11 and
13 with equations 5, 7 and 8. Specifically one obtains
and
where r represents the capacitor ratios a.sub.1, a.sub.2, b,
c.sub.11, and c.sub.2. Thus, the circuit of FIG. 4a illustrates an
excellent sensitivity behavior, with very low sensitivities to the
accurate and stable capacitor ratios r. Where
S.sub.GB.sup..omega..sbsp.o =1, .omega..sub.o is proportional to
GB, and GB must be carefully controlled and stabilized when
precision filters are required.
SPECIFIC EXAMPLE OF OPERATION
The filter performance is illustrated by the circuit in FIG. 5, a
special case of the implementation of FIG. 4a with an added MOS
output summing circuit 50. The transfer function V.sub.B /V.sub.i
and V.sub.L /V.sub.i are described by equations 9a and 9b with
equations 15a and 15b where C.sub.4 =C.sub.7 =0 and C.sub.5
=C.sub.6 =.infin.. Further, V.sub.H is a highpass output, resulting
in
and V.sub.o, derived from a buffered summer 50 using a CA3600 CMOS
Integrated Circuit, given a biquadratic transfer function, ##EQU3##
which can realize allpass, notch, or highpass filters. The latter
one, however, buffered or unbuffered, is more conveniently
implemented at the terminal V.sub.H. In equation 19, h=C.sub.s1
/C.sub.s4, d.sub.i =C.sub.si /C.sub.s1, i=2,3, and the gain of the
CMOS inverter is assumed to be infinite. The difference introduced
by this assumption is adjusted by C.sub.s4.
Using equations 9a and 9b, 15a and 15b, 17a, 17b, and 17c, and 19,
a bandpass and a notch filter were designed for the parameters
f.sub.o =900 kHz and Q.sub.R =15. Using GB.perspectiveto.2
.pi..multidot.3 MHz, .tau..perspectiveto.17 ns, and C.sub.in
.perspectiveto.4 pF results in the capacitors C.sub.1 =27 pF,
C.sub.2 =3.3 pF, C.sub.3 =3pF, C.sub.s1 =7.7 pF, C.sub.s2 =0.22 Pf,
C.sub.s4 =5.5 pF and C.sub.s3 =0. The response resulted in
predicted behavior.
Similarly, a lowpass and highpass filter were designed for the
parameters f.sub.3dB =1 MHz and Q.sub.R =1/.sqroot.2. The response
obtained with the capacitor values C.sub.1 =7.38 pF, C.sub.2 =3.3
pF and C.sub.3 =15 pF was in agreement with theory.
SUMMARY
The integrable analog active filter can be manufactured as a MOS
integrated circuit with the ratioed capacitors implemented into the
integrated circuit structure.
The process of connecting ratioed capacitors across integrated
circuit integrating amplifiers has been clearly set forth in the
previous paragraphs. Ratioed capacitors are easily implemented in
MOS integrating circuitry.
The integrable analog active filter is dependent on the parameter
GB which can be stabilized in integrated circuit form.
Stabilization, of course, is not critical in one useful and highly
important application requiring analog, and preferably integrable
circuits, that of antialiasing band limiting filters in
sampled-data or digital signal processing systems.
The filters can be made tunable or adjustable in discrete steps or
continuously by switching into or out of the circuits different
values of capacitors and-or by varying the integrator gains.
Various modifications can be made to the integrable analog active
filter of the present invention without departing from the apparent
scope thereof. The integrable analog active filters from the second
order filters disclosed in this patent application by way of
example and for purposes of illustration only, can be extended to
high-order filters via simulated ladders or multiple feedback
topologies.
* * * * *